Experimental approach for testing the uncoupling between cardiovascular variability series

In cardiovascular variability analysis, the significance of the coupling between two series is commonly assessed by defining a zero level on the magnitude-squared coherence (MSC). Although the use of the conventional value of 0.5 does not consider the dependence of MSC estimates on the analysis parameters, a theoretical threshold Tt is available only for the weighted covariance (WC) estimator. In this study, an experimental threshold for zero coherence Te was derived by a statistical test from the sampling distribution of MSC estimated on completely uncoupled time series. MSC was estimated by the WC method (Parzen window, spectral bandwidth B = 0.015, 0.02, 0.025, 0.03 Hz) and by the parametric autoregressive (AR) method (model order M= 4, 8, 12, 16), on time series with length L = 180, 300, 420, 540 s. Te decreased with increasing B and L and with decreasing M (range: 0.11-0.54 for WC estimator, 0.06-0.46 for AR estimator). Values for the typical parameter settings of WC and AR estimation (B = 0.025 Hz; M = 8; L = 300 s) were, respectively, 0.24 and 0.17. Moreover, Tt was always higher (range: 0.12-0.65) and the results were less dependable than those for Te in defining the zero level of MSC. Thus, with the proposed method, the hypothesis of uncoupling is rejected by accounting for the parameters that affect the confidence of spectral and cross-spectral estimates. The broad applicability of this approach should favour its introduction for assessing the significance of the coupling between cardiovascular variability series.